I was given the 1D heat equation
$\frac{\partial u}{\partial t}=u+\frac{\partial^2 u}{\partial x^2}$
with the boundary conditions of
$0 < x < \pi$ , $u(0,t)=0$ , $\frac{\partial u}{\partial x}(\pi,t)=0$ , $u(x,0)=f(x)$
I was then instructed to solve the BVP which I did, but I was also asked the following:
"Find the stead state solution if it exists"
If the 1D heat equation was just
$\frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial x^2}$
I could most definitely say yes there is a stead state solution and call $\frac{\partial u}{\partial t} = 0$ but since there is an added $u$ in the middle I am not entirely sure.
If there is a steady state solution I do not know how to approach it. Any help would be greatly appreciated!
Andrew